I think Wagner will continue in its form as an instrument of Russian foreign policy - as a provider of services to dodgy regimes - and as a cash cow: everyone gets a cut from Wagners income, Putin, MFA, MOD, all the elites - and it would suit all concerned to meet keep both the strategic Russian interests and the cash going.
I doubt Wagner will continue to play a role as a major combatant in Ukraine - those days are (imv) gone.
The Belarus thing is, I think, complicated - Prigozhin is a secure hotel room watching Netflix before leaning how to fly is one thing, but hoardes of his goons is something else. They could be asset, but they could also be a threat to the balance he manages. They might even to decide that if they couldn't get to Moscow, maybe they could get to Minsk...
Lukashenko walks a fine line - he has to please Putin, but he also has to manage a security establishment, a population, and the economic elites who really don't want to get involved in Ukraine - it's always about doing the minimum possible that Putin wants/needs, and I imagine Lukashenko wants Wagner charging across the border, and shattering the complex political situation he balances on like he wants a shovel through the head.